Electrophysiology catheters are designed for use in mapping and/or ablation of the heart. Electrophysiology catheters typically include a number of band electrodes mounted to the tip portion of the catheter shaft and a tip electrode at the distal end of the catheter shaft. To properly manipulate the electrodes against the target sites within a heart, the tip portion must be flexible and capable of being manipulated into a variety of shapes. U.S. patent application Ser. No. 5,487,757, entitled "Multicurved Deflectable Catheter, " the disclosure of which is incorporated by reference, discloses an electrophysiology catheter in which the tip portion can be deflected radially by pulling on a manipulator wire and also defected laterally by rotating a core wire which extends into the tip section. In addition to the manipulator and core wires, this patent discloses the use of an axially slidable stiffener wire, the distal end of which can be located at different positions along the tip portion to change the stiffness of the tip, and thus the general size of the curve in the tip.